Question

Determine the number of ways such that 5 men and 5 women be seated at a round table if no two women are seated together.

(a) 654870

(b) 144521

(c) 362160

(d) 5634

I have been asked this question during an interview.

The origin of the question is Counting in section Counting of Discrete Mathematics

Answer 1

Right option is (c) 362160

To elaborate: The men and women can be seated alternately so that no two women will sit together. Hence, 4 women can be seated on alternate seats at a round table in (4 – 1)! or 6

ways. Now, the 5 men can be seated in the remaining seats in 5! or 120 ways. Therefore the total number of ways in this case will be (10-1)! – (120 * 6) = 362160.